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%TCIDATA{Created=Tue May 11 19:33:24 2004}
%TCIDATA{LastRevised=Mon Aug 04 23:24:42 2008}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}

\begin{document}
La expresi\'{o}n $\ \dfrac{3x}{x^{2}-b^{2}y^{4}}-\dfrac{y}{x-by^{2}}%
+\dfrac{b}{x+by^{2}}$ se puede simplificar como:\newline \qquad a)
$-\dfrac{xy-xb-3x+by^{3}+b^{2}y^{2}}{\left(  x+by^{2}\right)  \left(
x-by^{2}\right)  }$b) $-\dfrac{xy+xb-3x+by^{3}-b^{2}y^{2}}{\left(
x+by^{2}\right)  \left(  x-by^{2}\right)  }\bigskip$\newline \qquad c)
$\dfrac{3x+xy-xb+by^{3}+b^{2}y^{2}}{\left(  x+by^{2}\right)  \left(
x-by^{2}\right)  }$\qquad d) $\dfrac{3x+xy+xb+by^{3}-b^{2}y^{2}}{\left(
x+by^{2}\right)  \left(  x-by^{2}\right)  }$

La expresi\'{o}n $\ \dfrac{3x^{2}}{x^{2}-b^{2}y^{2}}-\dfrac{y}{bx-b^{2}%
y}+\dfrac{1}{x+by}$ se puede simplificar como:\newline \qquad a)
$\dfrac{3x^{2}b-xy+xb-by^{2}-b^{2}y}{\left(  x+by\right)  b\left(
x-by\right)  }$\qquad b) $-\dfrac{3x^{2}b-xy+xb-by^{2}-b^{2}y}{\left(
x+by\right)  b\left(  x-by\right)  }\bigskip$\newline \qquad c) $\dfrac
{3x^{2}b+xy-xb+by^{2}+b^{2}y}{\left(  x+by\right)  b\left(  x-by\right)  }%
$\qquad d) $\dfrac{3x^{2}b-xy+xb-by^{2}-b^{2}y}{\left(  by-x\right)  b\left(
x-by\right)  }$

La expresi\'{o}n $\ \dfrac{3x^{2}}{5x^{2}-5b^{2}y^{2}}-\dfrac{y}%
{x-by}+\dfrac{a}{x+by}$ se puede simplificar como:\newline \qquad a)$\dfrac
{1}{5}\dfrac{3x^{2}-5xy+5xa-5by^{2}-5aby}{\left(  x+by\right)  \left(
x-by\right)  }\qquad$b)$-\dfrac{1}{5}\dfrac{3x^{2}-5xy+5xa-5by^{2}%
-5aby}{\left(  x+by\right)  \left(  x-by\right)  }\bigskip$\newline \qquad
c)$\dfrac{3x^{2}-5xy+5xa-5by^{2}-5aby}{\left(  x+by\right)  \left(
x-by\right)  }\qquad$d)$\dfrac{1}{5}\dfrac{3x^{2}+5xy-5xa-5by^{2}%
-5aby}{\left(  x+by\right)  \left(  x-by\right)  }$

La expresi\'{o}n $\ \dfrac{3x^{2}-27}{x^{2}-b^{2}y^{2}}-\dfrac{y}%
{8x-8by}+\dfrac{4a}{x+by}$ se puede simplificar como:\newline \qquad a)
$\dfrac{1}{8}\dfrac{24x^{2}-xy+32xa-by^{2}-32aby-216}{\left(  x+by\right)
\left(  x-by\right)  }$\qquad b) $-\dfrac{1}{8}\dfrac{24x^{2}-xy+32xa-by^{2}%
-32aby-216}{\left(  x+by\right)  \left(  x-by\right)  }\bigskip$%
\newline \qquad c) $\dfrac{24x^{2}-xy+32xa-by^{2}-32aby-216}{\left(
x+by\right)  \left(  x-by\right)  }$\qquad d) $\dfrac{1}{8}\dfrac
{24x^{2}-xy-32xa-by^{2}+32aby-216}{\left(  x+by\right)  \left(  x-by\right)  }$

La expresi\'{o}n $\ \dfrac{3x^{2}-3}{2x^{2}-2b^{2}y^{2}}-\dfrac{2y}%
{2x-2by}+\dfrac{a}{2x+2by}$ se puede simplificar como:\newline \qquad a)
$\dfrac{1}{2}\dfrac{3x^{2}-2xy+xa-2by^{2}-aby-3}{\left(  x+by\right)  \left(
x-by\right)  }$\qquad b) $-\dfrac{1}{2}\dfrac{3x^{2}-2xy+xa-2by^{2}%
-aby-3}{\left(  x+by\right)  \left(  x-by\right)  }\bigskip$\newline \qquad c)
$\dfrac{3x^{2}-xy+xa-2by^{2}-aby-3}{\left(  x+by\right)  \left(  x-by\right)
}$\qquad d) $\dfrac{1}{2}\dfrac{3x^{2}-xy+xa-2by^{2}-2aby-3}{\left(
x+by\right)  \left(  x-by\right)  }$

La expresi\'{o}n $\ \dfrac{5x^{2}}{7x^{2}-7b^{4}y^{2}}-\dfrac{2y}{x+b^{2}%
y}+\dfrac{a}{x-b^{2}y}$ se puede simplificar como: \bigskip\newline
\qquad\medskip a) \dfrac{1}{7}\dfrac{5x^{2}-14xy+7xa+14b^{2}y^{2}+7ab^{2}%
y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }\qquad b) \dfrac{1}%
{7}\dfrac{5x^{2}-14xy-7xa-14b^{2}y^{2}+7ab^{2}y}{\left(  x+b^{2}y\right)
\left(  x-b^{2}y\right)  }\newline c) \dfrac{5x^{2}-14xy+7xa+14b^{2}%
y^{2}+7ab^{2}y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  } \qquad d)
-\dfrac{1}{7}\dfrac{5x^{2}-14xy+7xa+14b^{2}y^{2}+7ab^{2}y}{\left(
x+b^{2}y\right)  \left(  x-b^{2}y\right)  }

La expresi\'{o}n $\ \dfrac{2x^{2}}{4x^{2}-4b^{2}y^{2}}+\dfrac{y}{x+by}%
-\dfrac{2a}{x-by}$ se puede simplificar como: \bigskip\newline \qquad\medskip
a) \dfrac{1}{2}\dfrac{x^{2}+2xy-4xa-2by^{2}-4aby}{\left(  x+by\right)  \left(
x-by\right)  }\qquad b) \dfrac{1}{4}\dfrac{x^{2}+2xy-4xa-2by^{2}-4aby}{\left(
x+by\right)  \left(  x-by\right)  }\bigskip\newline c) \dfrac{1}{4}%
\dfrac{x^{2}-2xy-4xa-2by^{2}-4aby}{\left(  x+by\right)  \left(  x-by\right)  }
\qquad d) \dfrac{1}{2}\dfrac{x^{2}-2xy-4xa-2by^{2}-4aby}{\left(  x+by\right)
\left(  x-by\right)  }

La expresi\'{o}n $\ \dfrac{5x^{2}}{3x^{2}-3b^{4}y^{2}}+\dfrac{y}{x-b^{2}%
y}+\dfrac{a}{x+b^{2}y}$ $\allowbreak$ se puede simplificar como:
\bigskip\newline \qquad a) \dfrac{1}{3}\dfrac{5x^{2}+3xy+3xa+3b^{2}%
y^{2}-3ab^{2}y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }\qquad b)
-\dfrac{1}{3}\dfrac{5x^{2}+3xy+3xa-3b^{2}y^{2}-3ab^{2}y}{\left(
x+b^{2}y\right)  \left(  x-b^{2}y\right)  }\bigskip\newline \qquad c)
\dfrac{5x^{2}-3xy+3xa+3b^{2}y^{2}-3ab^{2}y}{\left(  x+b^{2}y\right)  \left(
x-b^{2}y\right)  } \qquad d) \dfrac{1}{3}\dfrac{5x^{2}-3xy-3xa+3b^{2}%
y^{2}-3ab^{2}y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }

La expresi\'{o}n $\ \dfrac{7x^{2}}{6x^{2}-6b^{2}y^{4}}-\dfrac{3y}{x+by^{2}%
}-\dfrac{3a}{x-by^{2}}$ se puede simplificar como: \bigskip\newline \qquad a)
\dfrac{1}{6}\dfrac{7x^{2}-18xy-18xa+18by^{3}-18aby^{2}}{\left(  x+by^{2}%
\right)  \left(  x-by^{2}\right)  }\qquad b) \dfrac{1}{6}\dfrac{7x^{2}%
-18xy-18xa-18by^{3}-18aby^{2}}{\left(  x+by^{2}\right)  \left(  x-by^{2}%
\right)  }\bigskip\newline \qquad c) \dfrac{7x^{2}-18xy-18xa+18by^{3}%
+18aby^{2}}{\left(  x+by^{2}\right)  \left(  x-by^{2}\right)  } \qquad d)
-\dfrac{1}{6}\dfrac{7x^{2}-18xy-18xa+18by^{3}-18aby^{2}}{\left(
x+by^{2}\right)  \left(  x-by^{2}\right)  }

La expresi\'{o}n $\ \dfrac{4x^{2}}{5x^{2}-5b^{4}y^{2}}+\dfrac{y}{x-b^{2}%
y}-\dfrac{2a}{x+b^{2}y}$ se puede simplificar como: \bigskip\newline
\qquad\medskip a) \dfrac{1}{5}\dfrac{4x^{2}+5xy-10xa+5b^{2}y^{2}+10ab^{2}%
y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }\qquad b) \dfrac{1}%
{5}\dfrac{4x^{2}+5xy-10xa+5b^{2}y-10ab^{2}y}{\left(  x+b^{2}y\right)  \left(
x-b^{2}y\right)  }\bigskip\newline \qquad c) \dfrac{1}{5}\dfrac{4x^{2}%
-5xy-10xa-5b^{2}y^{2}+10ab^{2}y}{\left(  x+b^{2}y\right)  \left(
x-b^{2}y\right)  } \qquad d) -\dfrac{1}{5}\dfrac{4x^{2}+5xy-10xa-5b^{2}%
y^{2}+10ab^{2}y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }

La expresi\'{o}n $\ \dfrac{7x^{2}}{4x^{2}-4b^{2}y^{2}}-\dfrac{2y}{x-by}%
-\dfrac{a}{x+by}$ $\allowbreak$ se puede simplificar como: \bigskip
\newline \qquad a) \dfrac{1}{4}\dfrac{7x^{2}-8xy-4xa-8by^{2}+4aby}{\left(
x+by\right)  \left(  x-by\right)  }\qquad b) -\dfrac{1}{4}\dfrac
{7x^{2}-8xy-4xa-8by-4aby}{\left(  x+by\right)  \left(  x-by\right)  }%
\bigskip\newline \qquad c) \dfrac{7x^{2}+8xy-4xa-8by^{2}+4aby}{\left(
x+by\right)  \left(  x-by\right)  } \qquad d) \dfrac{1}{4}\dfrac
{7x^{2}-8xy+4xa+8by^{2}+4aby}{\left(  x+by\right)  \left(  x-by\right)  }

La expresi\'{o}n $\ \dfrac{5x^{2}}{6x^{2}-6b^{4}y^{2}}-\dfrac{y}{x-b^{2}%
y}+\dfrac{3a}{x+b^{2}y}$ se puede simplificar como: \bigskip\newline \qquad a)
\dfrac{1}{6}\dfrac{5x^{2}-6xy+18xa-6b^{2}y^{2}-18ab^{2}y}{\left(
x+b^{2}y\right)  \left(  x-b^{2}y\right)  }\qquad b) \dfrac{5x^{2}%
-6xy-18xa-6b^{2}y^{2}-18ab^{2}y}{\left(  x+b^{2}y\right)  \left(
x-b^{2}y\right)  }\bigskip\newline \qquad c) -\dfrac{1}{6}\dfrac
{-5x^{2}-6xy+18xa-6b^{2}y^{2}+18ab^{2}y}{\left(  x+b^{2}y\right)  \left(
x-b^{2}y\right)  } \qquad d) \dfrac{1}{6}\dfrac{5x^{2}+6xy-18xa+6b^{2}%
y^{2}-18ab^{2}y}{\left(  x+b^{2}y\right)  \left(  x-b^{2}y\right)  }

La expresi\'{o}n $\ \dfrac{3x^{2}}{7x^{2}-7b^{2}y^{4}}+\dfrac{3y}{x+by^{2}%
}-\dfrac{a}{x-by^{2}}$ se puede simplificar como: \bigskip\newline \qquad a)
\dfrac{1}{7}\dfrac{3x^{2}+21xy-7xa-21by^{3}-7aby^{2}}{\left(  x+by^{2}\right)
\left(  x-by^{2}\right)  }\qquad b) \dfrac{1}{7}\dfrac{3x^{2}%
+21xy+7xa+21by^{2}-7aby^{2}}{\left(  x+by^{2}\right)  \left(  x-by^{2}\right)
}\bigskip\newline \qquad c) \dfrac{1}{7}\dfrac{3x^{2}+21xy-7xa+21by^{3}%
+7aby^{2}}{\left(  x+by^{2}\right)  \left(  x-by^{2}\right)  } \qquad d)
-\dfrac{1}{7}\dfrac{-3x^{2}+21xy-7xa-21by^{3}+7aby^{2}}{\left(  x+by^{2}%
\right)  \left(  x-by^{2}\right)  }

La expresi\'{o}n $\ \dfrac{5x^{2}}{4x^{2}-4b^{2}y^{4}}+\dfrac{y}{x+by^{2}%
}+\dfrac{2a}{x-by^{2}}$ se puede simplificar como: \bigskip\newline \qquad a)
\dfrac{1}{4}\dfrac{5x^{2}+4xy+8xa-4by^{3}+8aby^{2}}{\left(  x+by^{2}\right)
\left(  x-by^{2}\right)  }\qquad b) \dfrac{5x^{2}-4xy-8xa-4by^{3}+8aby^{2}%
}{\left(  x+by^{2}\right)  \left(  x-by^{2}\right)  }\bigskip\newline \qquad
c) \dfrac{1}{4}\dfrac{5x^{2}+4xy-8xa-4by^{3}-8aby^{2}}{\left(  x+by^{2}%
\right)  \left(  x-by^{2}\right)  }\qquad d) -\dfrac{1}{4}\dfrac
{-5x^{2}+4xy+8xa-4by^{3}-8aby^{2}}{\left(  x+by^{2}\right)  \left(
x-by^{2}\right)  }

La expresi\'{o}n $\ \dfrac{4x^{2}}{3x^{2}-3b^{4}y^{4}}+\dfrac{2y}{x-b^{2}%
y^{2}}-\dfrac{a}{x+b^{2}y^{2}}$ se puede simplificar como: \bigskip
\newline \qquad a) \dfrac{1}{3}\dfrac{4x^{2}+6xy-3xa+6b^{2}y^{3}+3ab^{2}y^{2}%
}{\left(  x+b^{2}y^{2}\right)  \left(  x-b^{2}y^{2}\right)  }\qquad b)
\dfrac{4x^{2}-6xy-3xa-6b^{2}y^{3}+3ab^{2}y^{2}}{\left(  x+b^{2}y^{2}\right)
\left(  x-b^{2}y^{2}\right)  }\bigskip\newline \qquad c) -\dfrac{1}{3}%
\dfrac{-4x^{2}+6xy-3xa+6b^{2}y^{3}-3ab^{2}y^{2}}{\left(  x+b^{2}y^{2}\right)
\left(  x-b^{2}y^{2}\right)  } \qquad d) \dfrac{1}{3}\dfrac{4x^{2}%
-6xy-3xa-6by^{3}+3ab^{2}y^{2}}{\left(  x+b^{2}y^{2}\right)  \left(
x-b^{2}y^{2}\right)  }



\end{document}